Hi topband lovers
Some friends contact me with deep concerns about the next Bouvet DX expedition
receiver antenna called SALAD
<http://www.lz1aq.signacor.com/docs/active-wideband-directional-antenna.php>
Salad antenna
I understand the concerns, Bouvet on 160m is a lifetime opportunity for most
top-banders!
When Doug NX4D, me N4IS and Dr Dallas started to try to understand the
limitation of the new Waller Flag, the first big question was;
How small a loop antenna can be to receive weak signal on 160, or MW?
Dr. Dallas Lankford III (SK), measured the internal noise of a small loop.
15x15 FT on his quiet QTH, and wrote a paper with the derivation necessary to
calculate the thermal noise of a small loop. The study most important point was:
The sensitivity of small loop antennas can be limited by internally generated
thermal noise which is a characteristic of the loop itself. Even amplifying the
loop output with the lowest noise figure preamp available may not improve the
loop sensitivity if manmade noise drops low enough
The noise on Bouvet island will be very low, < -120 dBm at 500Hz, and for sure
the internal thermal noise of the prosed RX antenna will limit the reception of
weak signals on 160m, it may work on 80 and above, but for 160 m, it will be a set
up for failure.
Why not a single, trustable beverage antenna over the ice or snow?? Or a proved
K9AY or a DHDL??
Below is the almost good transcript of the original pdf Flag Theory, for the
long answer.
73’s
JC
N4IS
Flag Theory
Dallas Lankford, 1/31/09, rev. 9/9/09
The derivation which follows is a variation of Belrose's classical derivation
for ferrite rod loop antennas,
“Ferromagnetic Loop Aerials,” Wireless Engineer, February 1955, 41– 46.
Some people who have not actually compared the signal output of a flag antenna
to other small antennas have expressed their opinions to me that the signal
output of a flag antenna has great attenuation compared to those other small
antennas, such as loops and passive verticals. Their opinions are wrong. One
should never express opinions which are based, say, on computer simulations
alone, without actual measurements. The development below is based on physics
(including Maxwell's equations), mathematics, and measurements.
Measurements have confirmed that the flag signal to noise formula derived below is
approximately correct despite EZNEC simulations to the contrary. For example, EZNEC
simulation of a 15' square loop at 1 MHz predicts its gain is about +4 dbi, while on
the other hand EZNEC simulation of a 15' square flag at 1 MHz predicts its gain is
about –46 dBi. But if you construct such a loop and such a flag and observe the
signal strengths produced by them for daytime groundwave MW signals, you will find
that the maximum loop and flag signal outputs are about equal. Although somewhat more
difficult to judge, the nighttime sky wave MW signals are also about equal.
Also, the signal to noise ratio formula below for flag arrays has been verified
by manmade noise measurements in the 160 meter band using a smaller flag array
than the MW flag array discussed below. Several years ago a similar signal to
noise ratio formula for small un-tuned (broadband) loop antennas was verified
at the low end of the NDB band.
The signal voltage es in volts for a one turn loop of area A in meters and a signal
of wavelength λ for a given radio wave is
es = [2πA Es /λ] COS(θ)
where Es is the signal strength in volts per meter and θ is the angle between
the plane of the loop and the radio wave. It is well known that if an omnidirectional
antenna, say a short whip, is attached to one of the output terminals of the loop and
the phase difference between the loop and vertical and the amplitude of the whip are
adjusted to produce a cardioid patten, then this occurs for a phase difference of 90
degrees and a whip amplitude equal to the amplitude of the loop, and the signal
voltage in this case is
es = [2πA Es /λ] [1 + COS(θ)]
.
Notice that the maximum signal voltage of the cardioid antenna is twice the
maximum signal voltage of the loop (or vertical) alone.
A flag antenna is a one turn loop antenna with a resistance of several hundred
ohms inserted at some point into the one turn. With a rectangular turn, with
the resistor appropriately placed and adjusted for the appropriate value, the
flag antenna will generate a cardioid pattern. The exact mechanism by which
this occurs is not given here. Nevertheless, based on measurements, the flag
antenna signal voltage is approximately the same as the cardioid pattern given
above. The difference between an actual flag and the cardioid pattern above is
that an actual flag pattern is not a perfect cardioid for some cardioid
geometries and resistors.
In general a flag pattern will be
es = [2πA Es /λ] [1 + kCOS(θ)]
where k is a constant less than or equal to 1, say 0.90 for a “poor” flag, to 0.99 or more
for a “good” flag. This has virtually no effect of the maximum signal pickup, but can have a
significant effect on the null depth.
1- The thermal output noise voltage en for a loop is
en = √(4kTRB)
where k (1.37 x 10^–23) is Boltzman's constant, T is the absolute temperature (taken
as 290), (Belrose said:) R is the resistive component of the input impedance, (but also
according to Belrose:) R = 2πfL where L is the loop inductance in Henrys, and B is the
receiver bandwidth in Hertz.
When the loop is rotated so that the signal is maximum, the signal to noise
ratio is
SNR = es/en = [2πA Es /λ]/√(4kTRB) = [66Af/√(LB)]Es .
The point of this formula is that the sensitivity of small loop antennas can be
limited by internally generated thermal noise which is a characteristic of the
loop itself. Even amplifying the loop output with the lowest noise figure
preamp available may not improve the loop sensitivity if manmade noise drops
low enough.
Notice that on the one hand Belrose said R is the resistive component of the input
impedance, but on the other hand R = 2πL. Well never mind. Based on personal on hands
experience building small loops, I believe R = 2πL is approximately correct. What I
believe Belrose meant is that R is the magnitude of the output impedance. For a flag
antenna rotated so the signal is maximum, the signal to noise ratio is
SNR = es/en = 2[2πA Es/λ]/√(4kT√((2πfL)^2 + (Rflag)^2)B) = [322Af/√(√((2πfL)^2
+ (Rflag)^2)B)]Es .
Now let us calculate a SNR. Consider a flag 15' by 15' with inductance 24 μH at
1.0 MHz with 910 ohm flag
resistor, and a bandwidth of B = 6000 Hz. Then A = 20.9 square meters and SNR =
2.86x10^6 Es . If Es is in
microvolts, the SNR formula becomes SNR = 2.9 Es .
Any phased array has loss (or in some cases gain) due to the phase difference
of the signals from the two
antennas which are combined to produce the nulls. This loss (or gain) depends
on (1) the separation of the two
antennas, (2) the arrival angle of the signal, and (3) the method used to phase the
two flags. Let φ be the phase
difference for a signal arriving at the two antennas. It can be shown by
integrating the difference of the squares
of the respective cosine functions that the amplitude A of the RMS voltage
output of the combiner given RMS
inputs with amplitudes e is equal to e√(1 – COS( φ)) where e is the amplitude
of the RMS signal, in other
words,
A= 1
2π∫
0
2π
2 e2cost−costφ2dt=e21−cosφ
The gain or loss for a signal passing through the combiner due to their phase difference is thus
√(1 – COS( φ)).
Let us consider the best case, when the signal arrives from the maximum
direction. For a spacing s between the
centers of the flags, if the arrival angle is α, then the distance d which
determines the phase difference between
the two signals is d = s COS(α). If s is given in feet, then the conversion of d to
meters is d = s COS(α)/3.28.
The reciprocal of the velocity of light 1/2.99x10^8 = 3.34 nS/meter is the time
delay per meter of light (or radio
waves) in air. So the phase difference of the two signals above in terms of time is T
= 3.34 s COS(α)/3.28 nS
when s is in meters. The phase difference in degrees is thus φ = 0.36Tf = 0.36 f x
3.34 s COS(α)/3.28 where f is
the frequency of the signals in MHz. If additional delay T' is added (phase
shift to generate nulls or to adjust the
reception pattern), then the phase difference is φ = 0.36(T + T')f = 0.36f(T' + 3.34
s COS(α)/3.28) . If the
additional delay is implemented with a length of coax L feet long with velocity
factor VF, then the phase delay is
φ = 0.37f(L/VF + s COS(α))
where f is the frequency of the signal in MHz, s is in feet, L is in feet, and
α is the arrival angle.
2-
In the case of the flag array above in the maximum direction there are two
sources of delay, namely 60.6 feet of
coax with velocity factor 0.70, and 100 feet of spacing between the two flag
antennas. The phase delay at 1.0
MHz for a 30 degree arrival angle is thus
φ = 0.37 x 1.0 x (60.6/0.70 + 100 COS(30)) = 64.1 degrees.
Thus the signal loss in the maximum direction at 30 degree arrival angle due to
spacing and the phaser is
√(1 – COS( 64.1)) = 0.75 or 20 log(0.75/2) = –8.5 dB.
Now comes the interesting part. What happens when we phase the WF array with
dimensions and spacing given
above? The flag thermal noise output doubles (two flags), and the flag signal
output decreases (due to spacing
and phaser loss), so the SNR is degraded by 14.5 dB to SNR = 0.55 Es .
So a signal of 1.8 microvolts per meter is equivalent to the thermal noise
floor of the flag array.
On some occasions, when manmade noise drops to very low levels at my location,
it appeared to fall below the
thermal noise floor of the WF array. By that I mean that the characteristic
“sharp” manmade noise changed
character to a “smooth” hiss. To determine whether this was the case, I
measured the manmade noise at my
location for one of these low noise events at 1.83 MHz.
To measure manmade noise at my location I converted one of the flags of my MW flag array to a loop.
The loop was 15' by 15', or 20.9 square meters. I used my R-390A whose carrier (S) meter indicates
signals as low as –127 dBm. The meter indication was 4 dB. Then I used an HP-8540B signal
generator to determine the dBm value for 4 dB on the R-390A meter. It was –122 dBm. Now the
fun begins. The RDF of a loop for an arrival angle of 20 degrees (the estimated wave tilt of manmade
noise at 1.83 MHz) was 4 dB. So now manmade noise after factoring out the loop directionality was
estimated as –118 dBm.
Field strength is open circuit voltage equivalent, which gives us –112 dBm. I
measured MM noise on the R-390A with a 6 kHz BW. The conversion to 500 Hz is
–10 log(6000/500) = –10.8,
which gives us –122.8 or –123 dBm.
The conversion to 500 Hz was necessary in order to be consistent with the SNR
above which was calculated for a 500 Hz BW.
The loop equation is es = 2πAEs/lambda = 0.41 Es, and 20 log(0.41) = –7.7,
rounded off to - 8, so we have -115 dBm, or 0.40 microvolts per meter for my lowest levels
of manmade noise at 1.83 MHz in a 500 Hz bandwidth.
This seemed impossibly low to me until I came across the ITU graph at right.
Manmade noise at quiet rural locations may be even lower than 0.40 microvolts
per meter at 1.83 MHz. But what about the MW band? From the CCIR Report 322 we
find that the manmade noise field strength on the average is about 10 dB
higher at 1.0 MHz than 1.83 MHz, which would make it 1.26 microvolts per meter
at 1.0 MHz. Another 4 dB is added because of impedance mismatch between the
R-390A and the loop, which brings manmade noise up to 2.0 microvolts per meter
at 1.0 MHz. The RDF of one of these flags is about 7 dB, which lowers the
manmade noise to 0.89 microvolts per meter. Observations in the 160 meter band
do not seem to agree exactly with this analysis because flag thermal noise has
never been heard on the MW flag array. But it would not surprise me at all if
the flag array thermal noise floor were only a few dB below received minimum
daytime manmade noise and that measurement error (for example, calibration of
my HP 8640B) accounts for the difference between measurement and theory. Also,
observations with a flag array having flag areas half the size of the MW flag
elements in the 160 meter band do confirm the signal to noise ratio formula; in
this case, flag thermal noise does dominate minimum daytime manmade noise at my
location (0.40 microvolts per meter field strength measured as described above.
_________________
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